volume of an ellipsoid

-=nobody=-

Well, I have a small problem. I know the general formula for the volume of an ellipsoid. But I have a task to find it with the help of an integral. Can you explain me how to do this?

Curious3141

We've covered this before. http://www.physicsforums.com/showthr...lume+ellipsoid

And for the more special and simple case of a spheroid : http://www.physicsforums.com/showthr...ght=revolution

-=nobody=-

Thank you very much, the information is great.
And can you write the formula like in that post but for an ellipsoid where a, b and c are different.

siddharth

As Curious3141 already posted, in the link below, HallsofIvy explains it very well. What part do you not understand?

http://www.physicsforums.com/showthr...lume+ellipsoid

Curious3141

No, that's for a spheroid (two axes equal). For the general ellipsoid use the triple integral method. Of course the final answer comes out to a simple [tex]V = \frac{4}{3}\pi abc[/tex], it's just the derivation that's involved.

-=nobody=-

And can you please show me how we can receive this
[tex]V = \frac{4}{3}\pi abc[/tex]
from this
[tex]2c\int_{x=-a}^a\int_{y=-b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}}\sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}dydx[/tex]

And can we also use this method?